Kamal Hyder, Al Jazeera's correspondent in Islamabad, said: "The fighting is really intense [and] is concentrating on the lower part of the building, some of the basement and a cave complex, we're told."
An Al Jazeera source said Uzbek fighters, armed with grenades and RPGs, were putting up the fiercest resistance and were also suspected of holding women and children hostage.
Hyder said it was unprecedented that Pakistan's elite force would struggle from before dawn into the evening to defeat the fighters.
"But the army is saying they are in control of the situatuion, they have already taken 95 per cent control, and the fighting is now slow, because they say they want to save maxiumum lives," Hyder said.
Major General Waheed Arshad, the chief military spokesman, told reporters on Tuesday that the armed students were firing on security forces from the minarets.
"I would not say that they are following the teachings of the Prophet, but the warped version of their warped clerics"
Chris, Stockholm, Sweden
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"About three or four terrorists have occupied the minarets. They are violating the sanctity of the mosque," Arshad said.
He added that the northern part of the mosque was cleared, enabling several women in burqas and around 30 children to escape, but the fighting was still going on in the southern part.
Hundreds remained inside as soldiers went through the compound's 75 rooms one at a time, facing bitter resistance.
"It is a final push to clear the mosque of armed militants," Arshad said.
"We are taking a step-by-step approach, a very deliberate approach, to make sure there is no collateral damage unnecessarily," he told reporters.
Al Jazeera's Rageh Omaar said the mosque compound is a large and complex building which will take the military a long time to cover.
The army will have to go room by room in a thorough search for those still inside, he said.
He added that there was no sign of the armed students giving themselves up.
Pakistani forces began storming the mosque compound after negotiations to an end a bloody weeklong standoff broke down.
Arshad said security forces launched an operation at 4am (23:00 GMT on Monday) "to clear the madrasa of militants".
Chaudhry Shujaat Hussain, a former prime minister and ruling party leader who led negotiations with those inside, said the final effort to secure a peaceful solution had failed.
"I am returning very disappointed," he said.
The deal was believed to have been arranged after Hussain met Pervez Musharraf, Pakistan's president.
Security forces had previously held back from mounting a full-scale assault because of fears for the safety of women and children that they said were being held hostage by Ghazi.
Ghazi said he had nearly 2,000 followers with him and that no one was being held hostage.